Converting text math to TeX math (e.g. automatically filling in \left(, \right), \frac, etc)

Question

At some point, it occurred to me that another level of abstraction may be possible on top of LaTeX. For example, why should I type

\left( \frac{\frac{a}{b + c} \frac{w + \lambda}{z}}{x\left[ \frac{c_n}{d}\right]} \right)\left \{\frac{x_0}{y_0} : x_0 > 0 \right \}

when I could say the same thing, more compactly, with

({{a}/{b + c} {w + \lambda}/{z}}/{x[{c_n}/{d}]} ){{x_0}/{y_0} : x_0 > 0}

or even

({a/{b + c} {w + \lambda}/z}/{x[c_n/d]} ){x_0/y_0 : x_0 > 0}

Sure, conversion from the latter to the former may not be general enough for all use cases, but it should be okay for many of them. It's also somewhat easier to read/debug, what with the fewer words running around.

I think I am going to try to implement such a command, \textmath{...} in LuaTeX (the {} should not be a problem since the parentheses are supposed to be balanced) that does precisely this conversion. But before I attempt this, my question is: is there already a package that does something similar?

After all, I'd hate to reinvent the wheel, and I suspect this question may be also on some other peoples' minds.

Thank you!

Note: this question isn't about the macros that many TeX editors have, convenient as they may be. While they may allow you to perform the topmost expansion automatically, that does not help readability in the long-run :(

Answer 1

ConTeXt provides a calcmath module (short for calculator math) that partially implements what you want.

\usemodule[calcmath]

% Needed because there is a typo in the code what prevents auto scaling of
% delimiters
\startluacode
function moduledata.calcmath.tex(str,mode)
    context(moduledata.calcmath.totex(str,mode))
end
\stopluacode

\starttext
\displaycalcmath{cos(a/(b + c) log(w+λ)/z)}
\stoptext

gives

This module was meant to implement features present in calculator math, so it only supports a single style of parenthesis and does not support subscripts or superscripts, although it should be easy to add them.

The lua code is in x-calcmath.lua file in the context distribution. This code is from the early days of luatex (circa 2006), and if it were to be rewritten now, it will be written using lpeg rather than regexs. The x-calmath.lua file has a partial lpeg implementation that is commented out.